The lesson
Graphs of Functions
in the
Algebra II curriculum
gives a thorough introduction to graphs of functions.
For those who need only a quick review,
the key concepts are repeated here.
The exercises in this lesson duplicate those in
Graphs of Functions.
There are things that you can DO to an equation $\,y = f(x)\,$ that will change its graph.
Or, there are things that you can DO to a graph that will change
its equation.
Stretching, shrinking, moving up/down/left/right, reflecting about axes;
they're all covered thoroughly in the next few web exercises:
An understanding of these graphical transformations makes it easy to graph a
wide variety of functions,
by starting with a basic model and
then applying a sequence of transformations to change it to the desired function.
For example, after mastering the graphical transformations, you'll be able to do the following:
For your convenience, all the graphical transformations are summarized in the
GRAPHICAL TRANSFORMATIONS table below.
Given any entry in a row, you should (eventually!) be able to
fill in all the remaining entries in that row.
TRANSFORMATIONS INVOLVING $\,\boldsymbol{y}$ (note that transformations involving $\,y\,$ are intuitive) 

DO THIS TO THE PREVIOUS $y$VALUE  NEW EQUATION  NEW GRAPH  $(a,b)$ MOVES TO ...  TRANSFORMATION TYPE 
add $\,p$ subtract $\,p$ 
$y = f(x) + p$ $y = f(x)  p$ 
shifts $\,p\,$ units UP shifts $\,p\,$ units DOWN 
$(a,b+p)$ $(a,bp)$ 
vertical translation vertical translation 
multiply by $\,1$  $y = f(x)$  reflect about $x$axis  $(a,b)$  reflection about $x$axis 
multiply by $\,g$  $y = g\cdot f(x)$  vertical stretch by a factor of $\,g$ 
$(a,gb)$  vertical stretch/elongation 
divide by $\,g$  $\displaystyle y = \frac{f(x)}{g}$  vertical shrink by a factor of $\,g$ 
$\displaystyle \bigl(a,\frac{b}{g}\bigr)$  vertical shrink/compression 
take absolute value  $y = f(x)$  part below $x$axis flips up  $(a,b)$  absolute value 
TRANSFORMATIONS INVOLVING $\,\boldsymbol{x}$ (note that transformations involving $\,x\,$ are counterintuitive) 

REPLACE ...  NEW EQUATION  NEW GRAPH  $(a,b)$ MOVES TO ...  TRANSFORMATION TYPE 
every $\,x\,$ by $\,x+p\,$ every $\,x\,$ by $\,xp$ 
$y = f(x+p)$ $y = f(xp)$ 
shifts $\,p\,$ units LEFT shifts $\,p\,$ units RIGHT 
$(ap,b)$ $(a+p,b)$ 
horizontal translation horizontal translation 
every $\,x\,$ by $\,x\,$  $y = f(x)$  reflect about $y$axis  $(a,b)$  reflection about $y$axis 
every $\,x\,$ by $\,gx\,$  $y = f(gx)$  horizontal shrink by a factor of $\,g$ 
$\displaystyle \bigl(\frac{a}{g},b\bigr)$  horizontal shrink/compression 
every $\,x\,$ by $\,\displaystyle \frac{x}{g}\,$  $\displaystyle y = f\bigl(\frac{x}{g}\bigr)$  horizontal stretch by a factor of $\,g$ 
$(ga,b)$  horizontal stretch/elongation 
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
